Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session HL: Turbulent Boundary Layers III |
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Chair: M. Gad-el-Hak, Virginia Commonwealth University Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 8 |
Monday, November 20, 2006 2:00PM - 2:13PM |
HL.00001: The Mean-Velocity Profile of Turbulent Wall-Bounded Flows:\ The Debate Continues M. Buschmann, M. Gad-el-Hak The recent debate concerning the mean-velocity profile of turbulent wall-bounded flows has ruled out neither a log nor power law behavior. Furthermore, a Reynolds number dependence of the mean-velocity profile has not been excluded either. Clearly, a more complex functional form is needed to describe the profile. The generalized log law introduced by Buschmann \& Gad-el-Hak in 2002 is re-examined using more recent pipe flow data from McKeon et al.\ (2004). The zeroth-order solution shows good agreement with the data. However, analyzing the fractional difference of that solution reveals that a previously not considered dependence on both the Reynolds number and wall-normal coordinate still persists. Progressing to the second-order solution resolves both deficits fairly well. The generalized log law is then valid throughout the profile above $y^+ \approx$100--150, in perfect agreement with the data. The Reynolds number dependence of the two main parameters, the K\'arm\'an constant and the outer additive constant, are predicted up to fifth order. For moderate Reynolds numbers the parameters calculated with the zeroth-order solution are very close to the values proposed by Zanoun (2003) for channel flows. However, the K\'arm\'an constant shows slight Reynolds number dependence, which is in excellent agreement with a function for $\kappa$ proposed by Tennekes (1968). [Preview Abstract] |
Monday, November 20, 2006 2:13PM - 2:26PM |
HL.00002: Composite mean velocity profile for zero pressure gradient turbulent boundary layers Kapil Chauhan, Hassan Nagib, Peter Monkewitz A new composite form for the mean velocity profile in zero pressure gradient turbulent boundary layers is developed based on recent high Reynolds number data. The inner expression using a Pad\'{e} 45 expansion describes the profile in the sublayer and the logarithmic law of the wall. In accordance with the idea of a wake function, the outer expression is an exponential function which is added to the inner expansion. The composite profile satisfies all the necessary physical boundary conditions. The new profile is fitted to various experimental measurements to determine their respective $\delta$, $u_\tau$ and $\Pi$. The behavior of these parameters is found to be consistent with classical understanding. In addition, the composite velocity profiles of George \& Castillo [App. Mech. Rev. 1997] and Nickels [J. Fluid Mech. 2004] are also fitted to find their respective parameters. We find that all three composite forms agree remarkably well when fitted to data with equivalent accuracies. However, the extracted skin- friction velocity exhibits considerable disagreement. We find that the composite profiles based on the logarithmic form predicts accurate $u_\tau$ when compared to recent oil-film measurements. [Preview Abstract] |
Monday, November 20, 2006 2:26PM - 2:39PM |
HL.00003: Spectral Characteristics of High $Re$ Zero Pressure Gradient Turbulent Boundary Layers Hassan Nagib, Kapil Chauhan, Michael Hites One-dimensional spectra from data over the $Re_\theta$ range between 4,100 and 23,700 in a zero pressure gradient turbulent boundary layer are studied. Detailed spectra computed from long time series of the streamwise velocity reveal a bi-modal distribution of energy in the buffer layer close to the wall. This confirms that the large scale, low frequency, motions of the boundary layer are important in the dynamics of the near wall region. The spectra exhibit distinct trends in the inner, outer and overlap region of the boundary layer, over limits that are consistent with those found from the mean velocity profile. Near the wall, the high frequencies/small scales are characterized by the length $\nu/u_\tau$ and velocity $u_\tau$, reflecting the classical inner scales of mean velocity. Away from the wall, low frequencies/large scales spectra scale with the length scale $\delta$ and velocity scale $u_\tau$, which are again consistent with the classical outer scales of mean velocity. Based on the inner and outer scalings, a spectral model is developed, which exhibits all the characteristics found in experimental measurements across the boundary layer. Results for Reynolds number trends of $k^{-1}$ law, filtered time series and burst frequency will also be presented. [Preview Abstract] |
Monday, November 20, 2006 2:39PM - 2:52PM |
HL.00004: ABSTRACT HAS BEEN MOVED TO FM.00006 |
Monday, November 20, 2006 2:52PM - 3:05PM |
HL.00005: On numerical and physical boundary conditions for high Reynolds number large-eddy simulation of wall-bounded turbulent flows C. Pantano, D.I. Pullin, P.E. Dimotakis We present results of an integrated subgrid modeling and numerical formulation for coarse-resolution, large-eddy simulations of attached, wall-bounded turbulent flows. The modeling approach is based on a combination of the stretched-vortex subgrid model (in the bulk of the flow) with a localized wall-function treatment that relates the instantaneous wall-parallel velocity to the shear stress at the wall. The formulation minimizes numerical errors introduced by the boundary condition treatment while preserving the physical elements required to reproduce the low-order statistics of these flows. The impermeability boundary condition is built into the method such that only the outer-flow solution is simulated and the inner region is modeled. The only allowed physical parameters of the model are those arising from the ``law of the wall,'' explicitly used as part of the closure. Damping functions, a common feature of closures at this level of description, are not used. Simulation results of turbulent channel flow are presented up to Reynolds number based on wall-friction velocity of $10^6$. These are in substantial agreement with experimental data. Further statistical results of the flow and inner region modeling will also be presented. [Preview Abstract] |
Monday, November 20, 2006 3:05PM - 3:18PM |
HL.00006: DNS of turbulent channel flows with boundary roughened with Alberto Scotti A method to simulate the effects of a roughened surface on a turbulent boundary layer is introduced. The method is easy to implement, does not increase the numerical overhead of the code and affects the mean velocity in an \textit{a priori} predictable way. A single parameter $k$ is sufficient to fully characterize the roughness. The procedure has been tested in turbulent channel flows at $Re_\tau=1000$, with roughness heights $k^+$ spanning the transitional regime. The properties of the rough flow agree well with experimental data. [Preview Abstract] |
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